Beginner DSLR camera

I am looking for a good lens for my D3400 camera. I am a beginner and don't understand much of the technical stuff. I just went on vacation and the pictures that I took with the lens that came with the camera are not the greatest.

I usually shoot either my kids in front of my house, indoors (rare), vacation pictures or sports.

I would like my pictures to have the blur in the background and take sharp photos

I was doing some research and it looks like one of these may be good Nikon AF-S FX NIKKOR 35mm f/1.8G or Nikon AF-S FX NIKKOR 50mm f/1.8G.

I don't understand the differences between D, FX, DX, G, etc. I think G is what I need for my camera to be able to auto-focus (based on what I'm reading)

Based on what I said I shoot can someone give me a recommendation? For the sports I'm usually in the bleachers. I have a zoom lens that unfortunately isn't the greatest but I don't think I can afford a new one of those right now.

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